Distributed Formation Control with Obstacle and Collision Avoidance for Hypersonic Gliding Vehicles Subject to Multiple Constraints

Procedure 1

Procedure of the calculation for the actual inputs.

Initialization: for HGV , Step 3 of Algorithm 1 is completed. Then, the virtual control signals and are obtained accordingly. Denote as the states of multiple HGVs at current time . and are the actual inputs to be solved at current time .

Step 1. Substitute into Eq. (62) to get .

Step 2. is obtained by applying and into Eq. (63). Then, can be calculated by Eq. (64) with the knowledge of and .

Step 3. According to Eqs. (65)–(68), and can be calculated.